According to the sampling theorem, a bandwidth required when an original signal is reconstructed from a received signal is more than two times larger than a signal bandwidth. However, when a compressive sensing technology is used, it is not always necessary to satisfy the sampling theorem. Therefore, the original signal can be reconstructed.
For example, in non-patent document 1, a technology by which the signals reflected from a plurality of objects can be reconstructed under an undersampling condition in a radar device is disclosed. FIG. 5 is a block diagram of the radar device which reconstructs the signals under the undersampling condition by using the compressive sensing technology.
The radar device shown in FIG. 5 includes a reception antenna 101, a demodulator 102, an integrator 103, an A/D converter 104, and a signal reconstruction unit 105. A modulated signal is received from a space by the reception antenna 101 and outputted to the demodulator 102. The demodulator 102 demodulates the received signal and outputs this to the integrator 103 as a demodulated signal. The integrator 103 compresses the demodulated signal by performing integration with a time of a sampling interval required for the reconstruction intrinsically. Further, the signal to be compressed is requested to be a chirp signal or a PN signal which has a good RIP characteristic. Hereinafter, a degree of integration when the demodulated signal is compressed by performing the integration is defined as a compression rate. Accordingly, the integrator 103 performs a compression process at the compression rate set in advance. Further, the signal which has been compressed is described as a compressed signal.
Here, the RIP characteristic is an index indicating whether or not the signal can be reconstructed that is disclosed in non-patent document 1 and is determined by a configuration for compressing the signal (in this case, the integrator 103) and the signal to be compressed (in this case, the demodulated signal).
The compressed signal from the integrator 103 is inputted to the A/D converter 104. When the integrator 103 outputs the compressed signal obtained by performing the integration with for example, four sampling intervals to the A/D converter 104, the sampling rate that is one-fourth of the intrinsically required sampling rate can be used in the A/D converter 104. Accordingly, the A/D converter 104 converts the compressed signal into the digital signal at this sampling rate and outputs the digital signal to the signal reconstruction unit 105.
In the signal reconstruction unit 105, by solving the “L1 norm minimization problem” described in non-patent document 1, the desired signal is reconstructed from the output value of the A/D converter 104. At this time, when a condition in which an amount of information of the desired signal is sufficiently small compared to the signal bandwidth and information is not lost when the signal is compressed is met, a correct reconstruction result can be obtained. For example, in the radar device, when the number of objects is sufficiently small in an observation range, such conditions can be met.